Example – 8 :Find the least Multiple of 7 which leaves a remainder of 4 when divided by 6, 9 15 and 18 ?

Sol : It can be find like above example

i.e LCM of 6 , 9 , 15 and 18 = 180.

Now find the series of LCM with remainder having 4

i. e 184, 364, ….. ( Here 7 is divisor of 364 )

So our answer is 364.

Example – 9 :Three bells ring at intervals of 5 seconds, 6seconds and 7 seconds respectively. If they toll together for the first time at 9AM in the morning, after what interval of time will they together ring again for thee first time.

Sol: Here we find Least Common Multiple (LCM) of 5, 6 & 7

i.e 5 x 6 x 7 = 210 ( here not having any common divisors in between two number out of all these numbers expect “1”. So multiplying all these numbers to get lcm)

Here our answer is 210 seconds.

Example – 10 :Find the LCM and GCD of 4/5, 5/6, 7/15 ?

Sol: Find the LCM of numerators (4 , 5 , 7 ) = 4 x 5 x 7 = 140 ( here not having any common divisors in between two number out of all these numbers expect “1”. So multiplying all these numbers to get lcm)